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Full text of "An 'average eye' for heterochromatic photometry, and a comparison of a flicker and an equality-of-brightness photometer"

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A11101 E^som 


A1 11 01 29501 4 

/Bulletin of the Bureau of Standards 

QC1 .U5 V14;1918-19 C.1 NBS-PUB-C 1905 



By E. C. Crittenden and F. K. Richtmyer 



I. Introduction 87 

II. Apparatus 89 

III. Measurements on the Ives-Kingsbury solutions for selection op 


i. Preliminary measurements on solutions 93 

2. Measurements to establish a normal characteristic ratio 95 

IV. Measurements on blue glasses 97 

V. Other measurements by selected observers 104 

1. On a blue solution representing the color difference of carbon and 

gas-filled tungsten lamps 104 

2. On a lamp giving the color of a pentane standard against 4 wpc 

carbon lamps 106 

3. On a blue solution and on multivoltage standards 107 

VI. Conclusion 109 

1. Effect of individual characteristics 109 

2. Comparison of flicker jjand equality-of -brightness photometers 11 1 


The work to be reported in this paper was undertaken in connec- 
tion with the committee on research of the Illuminating Engineer- 
ing Society. The reports of that committee * for 1914 give a 
general survey of photometric problems on which investigation is 
especially desirable. Following this general review, it was felt that 
the new committee appointed for 191 5 might most effectively 
stimulate investigation by choosing a particular field and arranging 
for experimental work in it. The field chosen was that of hetero- 
chromatic photometry. In order to accomplish something definite 
within the time available for the investigation it appeared desirable 
to confine the work within rather narrow limits, and it was decided 
to give attention primarily to the question of the methods to be 

1 Trans. 111. Eng. Soc, 9, pp. 307, 333, 345, 358, 505; 1914. 


88 Bulletin of the Bureau of Standards i\\,i. n 

used in actual photometric comparisons involving a color difference 
and to such phases of this question as could be studied in a single 

As a solution for the whole problem of photometry with a 
color difference the use of a flicker photometer under certain speci- 
fied conditions has been proposed in particular by H. E. Ives. 2 
To strengthen the position of the flicker instrument there has been 
developed also a complete scheme 3 for the choice of normal groups 
of observers, including the establishment of an "average eye." 
This proposed systematization of heterochromatic measurements 
appeared so definite and practical as to deserve a thorough trial. 

The present work, therefore, was planned to show the difference 
to be expected between individuals and to include readings by a 
large number of observers so as to establish average or normal 
values for various measurements involving color differences. 
In general, similar measurements were to be made on a flicker 
photometer and on an equality -of-brightness photometer in order 
to establish the relation between results obtained by the two 
methods and the relative certainty of measurements made by the 
two types of instruments. 

The experimental data to be presented were obtained in the 
laboratories of the Bureau of Standards during the summer 
of 191 5. Besides extensive preliminary tests, the data obtained 
include (1) readings by 115 observers on the Ives- Kingsbury 
test solutions for choice of observers, (2) measurements by the 
same observers on blue glasses presenting a color difference 
equivalent to that involved in comparing carbon lamps with 
vacuum tungsten lamps, (3) a repetition of the above measure- 
ments by a selected group of observers, (4) sets on a blue solution 
corresponding to the color difference between a carbon lamp and 
a gas-filled tungsten lamp, (5) a direct comparison of lamps 
operated at the color of the pentane lamp flame with others run at 
4 watts per candle, and (6) the calibration of a blue solution and 
measurements with it on lamps at various efficiencies. 

With the exception of the solution used in testing observers, it 
may be noted that the work has dealt only with color differences 
of the type given by two incandescent bodies at different tempera- 
tures, such as two lamps operated at different efficiencies. Lights 
showing this type of color difference are, of course, much more 

1 Phil. Mag. (6), 24, p. 852, 1912; Trans. 111. Eng.^oc, 10, p. 317, 1915. 
1 Ives and Kingsbury, Trans. 111. Eng. Soc, 10, p. 203; 1915. 

SSSSSJ] An Average Eye and Comparison of Photometers 89 

easily compared than those showing a more nearly "saturated" 
hue, but the difficulties are sufficient to impair very seriously the 
accuracy of many practical photometric measurements required 
at the present day. It is highly desirable that a method of com- 
paring the intensities of lights of different colors which can be used 
for all types of color difference should be agreed upon, but at 
present the field in which there is most urgent need of a high degree 
of accuracy in such comparisons is the rating of incandescent 
lamps. In the present investigation it has appeared desirable to 
make those tests which would have the most direct bearing upon 
the practical application of the instruments and methods involved. 


Two standard photometer bars were arranged as nearly as 
possible alike, on one of which a flicker photometer was used and 
on the other a Lummer-Brodhun photometer. In each case the 
photometer head was stationary and was illuminated on the left 
by a stationary lamp placed at such a distance as to give an 
effective brightness of about 2.5 millilamberts in the photometric 
field after allowing for all losses in the apparatus. A similar lamp 
on a carriage at the right was moved by turning a wheel beneath 
the photometer, and the cells and glasses referred to later were 
inserted on this side of the photometer so that a constant illumi- 
nation was maintained. Settings of the movable lamp were 
printed on a record sheet and were measured from reference lines 
on the sheet, proper allowance being made for the optical thick- 
ness of the cells. This method of recording settings is much 
quicker than reading from the bar; it also has the advantage of 
giving a permanent record free from the errors which are likely to 
be made in transcribing numerical readings. The mean of the 
groups of points can be located very quickly with a sufficient 
degree of accuracy. In these tests each observer was asked to 
keep a tally of the settings, which required taking the hand from 
the wheel which moved the lamp, as well as turning away from 
the photometer. 

The lamps used have double hairpin carbon filaments in one 
plane, and were operated at a voltage which made them match the 
color of the Bureau's 4 wpc standards. For the distances at 
which the lamps were used, the illumination given follows the 
inverse-square law with a sufficient degree of exactness so that no 
corrections were necessary. The voltage was controlled by 
potentiometers, f 


Bulletin of the Bureau of Standards 

[Vol. 14 

The flicker photometer used was a standard Lummer-Brodhun 
head with the rotating prism attachment described by E. F. 
Kingsbury. 4 The particular instrument used was very kindly 
loaned by Mr. Kingsbury. The photometer head was modified 
by removing the original prisms and putting in a pair of which 
one has two quadrants cut away so as to make the duration of 
exposure to each light the same. (See Fig. i, A.) In the flicker 
attachment as originally made the focal plane of the eyepiece fell 
considerably beyond the comparison prisms. By inserting a 
collar to extend the telescope the instrument could be made to 
focus on the face of the prisms, this arrangement being intended 
for use in making equality-of-brightness settings with the flicker 
prism at rest. A considerable number of trials indicated that for 

Photometric fields 

A . Type of field used in the flicker photometer. The small circle which one observes travels over the field 
as indicated. B. Lummer-Brodhun field used in the equality-of-brightness measurements. (Contrast 
type, not indicated by sketch.) The circle shows the part used for the small field, the remainder being 
covered by an illuminated diaphragm 

most observers this arrangement was decidedly better for flicker 
settings. Consequently it was used throughout the tests. With- 
out a very good photometric field this could not be done, since 
any imperfections in the field would cause flicker, but the prism 
used was sufficiently good so that with a color and intensity match 
there was practically no flicker in the field even at low speeds. 

A tachometer was attached to the flicker mechanism, and the 
speed was controlled by a rheostat in series with the motor. It 
was expected that each observer would have to choose a suitable 
speed for each color difference measured, but extensive trials 
with a number of observers showed that, over a limited range, 
change of speed had very little effect either on precision of setting 
or on the mean result. It was finally decided to adopt a moderate 
speed (12 light cycles per second) for all observers and all set- 

4 Jour. Franklin Institute, 180, p. 215; 1915. 

RiSyZ\ An Average Eye and Comparison of Photometers 91 

tings. Observers were then directed to set for a minimum of 
flicker. Although this speed was rather low for settings on the 
yellow solution and high for those with color match, few observers 
found serious difficulty in making definite settings. The constant 
speed was adhered to partly because in the preliminary measure- 
ments there had been indications of slight changes of results when 
speeds much higher or much lower were used, particularly with 
the yellow solution. 

On the second photometer bar measurements were made under 
two conditions — (1) with the standard Lummer-Brodhun con- 
trast field, (2) with an illuminated diaphragm which limited the 
field to about 2 , as in the flicker instrument. (See Fig. 1, B.) 
In the case of the contrast field, however, all observers were asked 
to make their settings by the middle strips, disregarding the con- 
trast trapezoids. The small field was used because it gave equality- 
of-brightness measurements under conditions closely similar to 
those used with the flicker instrument. It was also thought that 
limiting the field so as to use only a fairly homogeneous part of 
the retina might reduce variations in judgment and give settings 
more truly characteristic of the observer's eye. 

All the photometers used had pupil apertures 5 mm in diameter. 
Each photometer head was provided with holders for absorption 
glasses, as well as holders for absorption cells, especially con- 
structed to prevent any diffusion of stray light into the photo- 
metric field. 

Three pairs of 1 cm cells were provided. These were constructed 
practically like those described by Ives and Kingsbury, 5 with 
removable sides of colorless optical glass. A small modification 
which was found to facilitate secure sealing of the sides was made 
by beveling slightly each edge of the cell blocks, thus making a 
groove to be filled by the paraffin seal. Although the sides were 
made of polished plate glass, it was found that there were appre- 
ciable differences between the transmission of different plates. 
Repolishing of the plates, which was necessary after using some 
solutions, also changed the transmissions perceptibly. The differ- 
ences and the changes mentioned were less than 1 per cent, but 
were not negligible for precise work. So far as color is concerned, 
the glass used was satisfactory. It had been obtained for other 
work, requiring very clear glass, and its applicability for the pres- 
ent purpose was tested directly by measuring its transmission for 

5 Trans. 111. Eug. Soc, 9, p. 795; 1914. 

92 Bulletin oj the Bureau of Standards [Voi.i 4 

the two extreme colors of light to be used — that is, the light trans- 
mitted by the two test solutions. Its transmission for the two 
was the same within 0.2 per cent. 

Considerable time was given to experiments with the cells to 
determine how closely conditions could be reproduced. In brief, 
it may be said that results can be rather easily reproduced to 
within 1 per cent with them, but if an accuracy greater than one- 
half per cent is desired, extreme care is necessary. In any case 
thorough cleaning is essential, and it is desirable to compare the 
cells with each other after each cleaning. 

The paraffin used for sealing the cells is somewhat difficult to 
remove completely from the plates, and a supply of hot, running 
water is almost a necessity for thorough cleansing. Xylol also is 
a convenient solvent of paraffin and is especially useful when the 
supply of hot water is not plentiful. 

Cells should be rilled well up to the neck, for if a meniscus of 
considerable size is left an appreciable amount of light may be 
reflected from it into the field. 


The method of selecting observers, to which reference has been 
made,® is based on determinations of the relative transmission of 
two solutions — one reddish yellow, the other blue-green. These 
are solutions, in water, of potassium bichromate and of copper 
sulphate, containing, respectively, 72 and 53 grams of the salt per 
liter of solution. While not definitely specified in the original pro- 
posal, it has been assumed that the solution is to be made up 
at 20 C, and that by copper sulphate is meant the crystals 
CuS0 4 + 5H.O. 

When measured at 20 C by the "average eye" with a flicker 
photometer conforming to specifications previously mentioned, 1 
cm layers of these two solutions were intended to have equal 
transmissions for the light of a carbon lamp of the standard 
4-watt-per-candle color. The average eye thus defined was origi- 
nally established by measurements made by 61 observers on the 
transmission of a green solution. 7 The two solutions above 
described were worked out later on the basis of measurements 
made by selected groups of observers. It is not at all clear that 
an average established by comparing the middle of the spectrum 

• Trans. 111. Eng. Soe, 10, pp. 203-208; 1915. ' Ives and Kingsbury, Phys. Rev. (2), 0, p. 230; 1915. 

RkSyZ] An Average Eye and Comparison of Photometers 93 

with the whole spectrum can be legitimately thus transferred by 
a few observers to the basis of a comparison of the two ends of 
the spectrum. For instance, it is known that an observer may 
be abnormally sensitive or nonsensitive in the middle of the spec- 
trum and yet appear normal in the comparison of the two halves 
of the spectrum, or he may be normal according to the first test 
and not so by the second. In fact, it would appear that tests of 
both kinds should be included in choosing observers for measure- 
ments of illuminants which show marked selectivity in the visible 
spectrum. Ives and Kingsbury state, however, that groups of 
observers selected by one criterion were found to satisfy the 
other. For the types of color difference with which the present 
investigation has been most directly concerned the two-solution 
test appeared most significant, besides being more convenient than 
the earlier one. This method alone, therefore, has been used for 
testing observers, and the characteristics of a given observer will 
be supposed to be represented by the ratio of the transmission 
of the yellow solution to that of the blue solution, as measured by 
that observer, although it is recognized that this ratio is more 
strictly an index of the observer's sensitiveness to lights in which 
different proportions are contributed by the two ends of the 


The standard temperature for the solutions is 20 C. The 
greater part of the present work was done at temperatures ranging 
from 25 ° to 30 , and, consequently, it was necessary to determine 
the temperature coefficients of the transmission of the test solu- 
tions. Over the range considered the variation with temperature 
was found to be practically linear. The transmission of the 
potassium-bichromate solution decreased nearly 0.2 per cent per 
degree rise of temperature, while that of the copper-sulphate solu- 
tion decreased about half as much. The differential correction 
to be applied to the ratio of the two transmissions was, therefore, 
practically 0.1 per cent per degree centigrade, the observed ratio 
(Y/B) being too small when the temperature was above 20 . 

Other conditions which affect the value of the ratio obtained 
are the color of the light for which the transmissions are measured 
and the brightness of the photometric field. The color is supposed 
to be that of the standard 4 wpc carbon lamp and ilic effective 
brightness 2.5 millilamberts (equivalent to an illumination of 25 

94 Bulletin of the Bureau of Standards [Vol. i 

meter-candles on a perfectly diffusing and completely reflecting 
surface) after allowing for losses in the photometer. In the par- 
ticular instruments used these losses aggregated nearly 50 per 
cent, so that the actual illumination necessary was about 50 

On account of the lack of a convenient nomenclature, as well 
as the difficulty of absolute determinations of diffuse reflectivities 
of surfaces, there has been some confusion as to the exact field 
brightness used in various investigations. In making the meas- 
urements recorded in this paper the effective brightness used was 
very close to 2.5 millilamberts; that is, the brightness produced 
by an illumination of 25 meter-candles on a perfectly diffusing 
and completely reflecting surface. The numerical values for the 
test ratios originally given before the Illuminating Engineering 
Society 8 were reduced, however, to the basis of an illumination 
of 25 meter-candles on a white surface having a reflectivity of 
approximately 90 per cent. Since a specification of the absolute 
brightness is preferable, 2.5 millilamberts is here retained as the 
standard brightness, and test ratios are given in this paper on 
that basis. The difference is quite unimportant, since the 
correction previously applied to the ratios was only 0.003. 9 

Since the variation of results arising from changes in the effi- 
ciency of the lamp or in the illumination used is small, no very 
precise determination of the effects of such changes has been made. 
Some measurements were made, however, with a lamp operated 
at 3.1 and at 5 watts per candle and with effective illuminations 
of approximately 10 and 50 meter-candles. In accordance with 
the reversed Purkinje phenomenon shown by the flicker photom- 
eter, 10 it was found that the ratio of transmissions (yellow -f- blue) 
was smaller at the higher illuminations. At 50 mc the average 
of three observers gave a ratio slightly over 1 per cent lower than 
the normal, while at 10 mc the ratio was 2 per cent higher than 
normal. A rise in the efficiency of the lamp naturally causes a 
decrease in the observed ratio, but the variation is so small that 
the effect of any error likely to occur in the rating of the lamp 
would be entirely negligible. Running the lamp at 3.1 wpc, or 
at 5 wpc, instead of 4, causes a departure from the normal ratio of 
only 1 to 2 per cent. It may be well to record that the funda- 

8 Trans. 111. Eng. Soc., 11, p. 331 (also note, p. 333); 1916. 

9 Thus, in the earlier paper the average observed ratio 0.987 was "corrected" to 0.990, whereas in either 
case the round number 0.99 may as well be used for all practical purposes. Fig. 6, in which the change 
would be scarcely perceptible, has not been redrawn. 

10 Ives. Trans. 111. Eng. Soc.. 5, p. -1-, i?:o; Phil. Mag. (6), 24, p. 170, 1912. 

Rkhtmy£\ An Average Eye and Comparison of Photometers 95 

mental 4 wpc carbon standards have oval-anchored filaments, 
and since their average reduction factor is 0.825 the standard 
efficiency is 4.85 watts per spherical candle or 2.6 lumens per watt. 
The color of the light is practically the same as that given by a 
vacuum tungsten lamp at 3.1 wpc or 3.2 lumens per watt. 

The composition of the test solutions is such that there is no 
reason to expect any difficulty in reproducing them or any change 
with time. Cells used for several months during the investiga- 
tion showed no appreciable change in transmission. 


In order to obtain an independent check on the average eye as 
defined by the test solutions and to test the characteristics of ob- 
servers to be used in later measurements, and at the same time to 
establish the relation between the characteristic ratio and some 
measurement met with in practical work, a series 01 measurements 
was made by 115 observers. On each photometer this series con- 
sisted of 8 sets of 10 readings each. On the flicker photometer 
sets were made on the two lamps at color match and on the same 
lamps with a blue-glass screen and with cells containing the two 
test solutions interposed in succession on one side of the photom- 
eter head. The four sets were immediately repeated in different 
order. The data given, therefore, are the mean results of 20 set- 
tings of the photometer on each condition. 

The original plans were to include a similar series of measure- 
ments on the equality-of -brightness photometer, but with it only 
the most experienced observers could make any definite settings 
on the test solutions, and even they varied so greatly from day to 
day that the results were quite useless as an indication of the ob- 
server's color characteristics. For instance, ratios determined on 
one day by the mean of several hundred settings could not be re- 
peated within 10 per cent on the next day, although the same ob- 
servers could reproduce their ratios day after day on the flicker 
photometer with an average deviation of less than 1 per cent, 
only 20 settings being made on each solution. Consequently, the 
equality measurements were made only on the smaller color differ- 
ences, such as that presented by the blue-glass screen, for which 
the results are given in the next section. One observer was unable 
even then to make settings definite enough to be used, and his re- 
sults are consequently not included in the following data, although 
his flicker settings were good. 

20172°— 17 7 

9 6 

Bulletin of the Bureau of Standards 

[Vol. 14 

With very few exceptions the observers included in these meas- 
urements are men who have had some years of experience in 
physical or chemical observations, and nearly 30 of them have had 
considerable recent practice in some sort of photometric measure- 
ments. The distribution of 1 1 4 observers with respect to charac- 
teristic ratio (Y-j-B) is shown in Fig. 2, where the ordinates rep- 
resent the number of individuals falling within a range of 1 per 
cent. For example, between 0.900 and 0.909, inclusive, there are 
5 observers. Such frequency curves must be used with caution, 






•2 c 











Fig. 2. — Distribution of 114 observers with respect to characteristic ratio (ratio of trans- 
mission of yellow test solution to that of the blue solution) 

The ordinates show the number of observers falling in a range of in ratio. The black rectangles repre- 
sent " color blind ' ' observers 

since their shape can often be greatly changed by grouping in 
different ways. In this case the number of individuals must be 
considerably increased before it can be told with certainty whether 
the unsymmetrical shape of the curve is accidental, but there is a 
marked indication of the existence of a fairly definite type of eye 
which gives systematically high ratios in the neighborhood of 1.10 
to 1 . 1 2. The solid black rectangles represent three men who were 
found to be definitely color blind in a test made by I. G. Priest with 
Nagel test cards. Some others in this group are known to have 

RkhtmytlA An Average Eye and Comparison of Photometers 97 

peculiarities in their color perception, although they are able to 
pass color-vision tests. 

The arithmetical average of the 114 ratios is 0.987. If the 
three observers classed as color blind are omitted, the average is 
0.983, but actually the line between normal and abnormal color 
vision is very difficult to draw. Moreover, the relation between 
color and luminosity is not very definite, and in making up an 
average luminosity scale there is little justification for ignoring 
that percentage of the people who are color blind. On the other 
hand, taking an average may give undue weight to the abnormal 
observers, and there is some advantage in taking instead of the 
average the median value; that is, a value such that there are 
equal numbers of observers above and below it. In this case the 
median for the 114 ratios is 0.977, and the effect of omitting the 
three extreme observers mentioned is only to make the median 
fall between 0.976 and 0.977. To show how closely groups 
selected at random might be expected to agree on the ratio, 
these 114 observers were arranged alphabetically and for each 
half of the list the mean and the median values were found. 
The two means were 0.982 and 0.992; that is, 1 per cent different. 
The two medians were 0.975 and 0.979, or 0.4 per cent different. 
In other words, in reproducibility the median appears to be some- 
what better than the mean. Even if the three color-blind observ- 
ers are omitted, the means of the two groups still differ by 0.8 per 
cent, being 0.979 and 0.987. 

In order to test the constancy of the characteristic ratio of 
individuals, 20 observers repeated their measurements at the end 
of the test. The average' deviation of an individual from his 
first value was 1 per cent, and the mean of the 20 differed by 0.2 
per cent in the two sets. Repeated measurements during the 
several months occupied by other parts of the work have indicated 
that this is the amount of variation to be expected in successive 
sets. Consequently, the average deviation of an experienced 
observer from his mean value is usually well below 1 per cent. 
No definite indications of any important change in an individual's 
ratio have been found. 


The blue glasses mentioned presented a color difference equiva- 
lent to that between a 4 wpc carbon lamp and a vacuum tungsten 
lamp at about 1.2 wpc (8.2 lumens per watt). In other words, 


Bulletin of the Bureau of Standards 

when the glass was placed in front of a carbon lamp the light 
transmitted was similar in color to that from a tungsten lamp, 
and it was compared with unmodified light from another carbon 
lamp. On such glasses measurements were made by all the ob- 
servers with the flicker photometer and with the two forms of 
equality field. The latter both showed large variations in results, 
and the general result is perhaps better shown by averaging out 
some of the individual errors. In order to do this the observers 



■lotion between observed transmission ■ of blue glass (jG) and characteristic 



to that between 4 wpc carbon fampB aac 1 1 ';c 

::r :^» 

were arranged in the order of their characteristic ratios and aver- 
aged in groups. Three of the extreme groups consist of 12 ob- 
servers each, the others of 13. The results are shown in Fig. 3. 
The flicker photometer data are plotted at the bottom, and for 
comparison the curve drawn to represent them is reproduced in a 
broken line along with the data for the two equality fields. The 
curves drawn represent the least square solutions for the whole 
114 observers, assuming a linear relation between characteristic 

RkkimyZ] An Average Eye and Comparison of Photometers 


ratios and observed transmissions. In the flicker measurements 
the change in transmission corresponding to i per cent difference 
in ratio is 0.13 per cent, while the other curves show correspond- 
ing changes of o. 1 1 and 0.12 per cent. 

The observers were somewhat arbitrarily classified by inspec- 
tion of their settings on the equality photometer with regard to 
the consistency of settings (not their accuracy), and in Table 1 
are given the mean results of the three classes, " a " meaning good, 
" b " medium, and " c " poor sets. The transmissions are all reduced 
to the basis of the mean ratio (0.987) so as to be strictly compara- 
ble, and the residuals are departures from the curves of Fig. 3; 
that is, the systematic errors due to individual characteristics 
have so far as possible been eliminated and the residuals represent 
largely the accidental errors in judgment. All transmissions given 
in this paper are for light of the quality given by a 4 wpc carbon 


table 1 

Transmission of Blue Glass (3G) and Residual Errors (114 Observers) 

of ob- 


Mean residuals (per cent) 



Equality photom- 


Equality photom- 








. 5414 

0. 5404 
















To test the reproducibility of results 20 observers well dis- 
tributed with respect to ratio, 12 of whom had had considerable 
photometric experience, were selected to repeat these measure- 
ments. The individual observations are shown in Fig. 4, in which, 
as before, the flicker curve is drawn through the other data for 
comparison. The average values for the transmission are given 
in Table 2. 

ioo Bulletin oj the Bureau oj Standards 


Transmission of Blue Glass (3G)— Two Sets by 20 Observers 



Equality photometer 

Large field 

Small field 

First set 









Average difference between two sets by each observer (per cent) 




Both groups of better observers in Table i find the transmission 
of the blue sdass smaller with the small field than with the larsre, 




.92 .96 LOO 104 


W. Tib 

Fig. 4. — Transmission of blue glass (jG) — two sets by each of 20 observers 

The crosses represent measurements with a standard Lummer-Brodhun photometer, the dots those with 
a small field. For this group of measurements the average results with these two fields were the same. 
(See Table 2.) The dashed line is the flicker curve 

which is to be expected, but obtain higher values with the flicker 
than with either form of equality field. The 20 who were chosen 
to repeat the measurement happen, however, to read, on the aver- 

Rkhtmnr] An Average Eye and Comparison of Photometers 101 

age, higher on the equality fields. The number of sets made is by- 
no means sufficient to establish standard values with the equality 
photometer, and a better approximation to the real "average" 
transmission can perhaps be obtained by omitting the observers 
whose sets were not consistent. Six of the 20 observers in the 
second set obtained results on one or both of the equality fields 
which differed by 2 per cent or more from their first sets. If these 
six are omitted, the means of the remaining 28 measurements are as 
shown in the last line of Table 2. 

With practice most observers tend to fix upon a more definite 
concept with regard to what constitutes equality of brightness 
between two different colors, and the question has been asked 
whether experienced observers obtain the same result as inexpe- 
rienced ones. Naturally the practiced observer can make more 
precise settings. In other words, to reproduce results with a given 
percentage of accuracy the unpracticed observer must make more 
measurements, but it does not appear that this fact gives any 
reason for expecting a systematic difference between results 
obtained by experienced observers and those obtained by inex- 
perienced persons. However, of these 114 observers the ones who 
might be classed as experienced in photometry did get a result 
slightly higher than the others. Twenty-two observers were 
selected as having had such experience as would justify giving 
extra weight to their sets if the purpose of the paper was to estab- 
lish normal values for the Lummer-Brodhun photometer, and their 
results follow in comparison with the mean of all the observers. 

Transmission of Blue Glass (3G) 



Equality photometers 

Large field 

Small field 


0. 5434 

0. 5425 

0. 5396 

22 " experienced " 


Among these 22 experienced observers are included half of the 
group whose results are given in Table 2, but the agreement 
between the two groups would not be materially affected if the ob- 
servers common to the two were omitted. 

Table 1 by itself would indicate a high degree of certainty in the 
transmission as determined by the large-field equality photometer, 

102 Bulletin oj the Bureau of Stand {Vci.i 4 

but this certainty is reduced by the failure of the 20 observers to 
repeat their or to agree with the larger group. Nearly half 

of the change shown by the 20 observers is due to one very poor 
set. but of these 20 observers the 14 who repeated results most 
consistently got a value o. 7 per cent above the mean of all the 
observations, and this higher value is corroborated by the other 
experienced observe 

As the result of the 134 measurements, the unweighted aver- 
age values for the transm: tins glass are 0.545 lor both 
flicker and large-field equality and 0.541 for the small-field equality 
photometer, but in general the observations here recorded leave 
an uncertainty of the order of 1 per cent in the values to be 

:- I I r measurements by the equality photometer. Further 
measurements, discussed in a later section, indicate that the 
values obtained by the mo: stent and the more experienced 

observers Tables 2 and 3) are nearer the result which would be 
obtained by increasing greatly the number of observations. 
The 22 observers whose Lummer-Brodhun settings should have 
mos: it on the score : -nee obtain practically the 

same result with the two small fields flicker and equality) and 
about one-half per cent hk tfa the large field. In searching 

for s .--11 differences, however if is sometime? misleading to 

take ave I a small number of oc 5 without considering 

the individual observations, for if most of the observers get small 
differences, a few erratic observers row the average results 

to one side or the other. Comparing the two small fields of these 

.^"her on the flicker and 11 higher on the 
equality. As between re-field equality and the flicker 

read higher on the former and 9 higher on the latter. While there 

iefinite preponderance in the one direction, it is evident that 

magnitude of the difference is not established with much 
accura : 

^idlekauff and Skogla:: iy called attention to 

the relation between the above values and those obtained in 
several ^oratories. This glass has a transmission 1.6 per 

cent gre an the glass 3B included in their compare, 

measurements, and if the values assigned for 3B are correspond- 
ingly increased for comparison with the preceding (0.543), the 
llts in different laboratories arc with a flicker photom- 

and 0.546. 0.551. and 0.552 -Brodhun pho- 


>^c. 11, p. 164. 19x6; this BnDedn. H Paper Xo. *77- 

RkhtmyH An Average Eye and Comparison of Photometers 103 

There are two differences in conditions which may in part 
account for the fact that the result obtained in the present work 
is below all the other Lummer-Brodhun values. In this work the 
photometer was used as an "equality" rather than a "contrast" 
field, and the illumination was much higher than that used in the 
other measurements. The difference probably arises, however, 
more from the fundamental uncertainty of equality-of -brightness 
measurements than from any of these systematic differences in 

Whether or not there is a systematic difference between the 
results obtained by contrast settings and those given by strictly 
equality settings can not be told except by testing a large number 
of observers, for on changing the method of judgment each observer 
must to a considerable extent reestablish his " definite concept " of 
what constitutes a setting, and some observers change in one direc- 
tion, some in the other. In general, the mean result obtained by 
a group of observers does not seem to be changed definitely in 
either direction by changing the method of judgment. When 
there is a considerable color difference in the field, some observers 
can set more definitely if the contrast strips are removed. In 
this case the strips were not removed, but observers were asked 
to disregard them so far as possible and to set for equality of 
brightness in the central strips of the field. It is to be noted that 
the 22 "experienced" observers setting this way obtain exactly 
the same average result as Middlekauff and Skogland's group set- 
ting by contrast. 

The greater certainty of the flicker values is shown by a compari- 
son of the mean residuals in Table 1 and the differences between 
sets in Table 2. It may be remarked that some observers with 
practice develop the ability to repeat values very closely on the 
equality photometer, and such observers would make a much bet- 
ter showing for that photometer in a comparison like that of Table 
2. Unfortunately, however, such observers are comparatively 
rare and do not in all cases settle on a value in agreement with 
their characteristics as indicated by the flicker method. 

Of the equality-of -brightness photometers the small field shows 
no material superiority over the large one. Table 2 would seem 
to indicate that it gave more reproducible results, but in Table 1 
it will be seen that the residuals average the same for the two 
forms, while the small field shows the poorest agreement between 
groups of observers. The use of the small field was discontinued 
after this test, because it gave no promise of any practical advan- 

io4 Bulletin of the Bureau of Standards [va.14 

tage. The data obtained are sufficient to indicate that if the 
small field had been carried through the measurements on the 
larger color differences the results would almost certainly have 
agreed with the flicker values more closely than the large-field 
measurements did. Practically, however, with these larger dif- 
ferences equality-of-brightness settings show such large varia- 
tions from time to time and such wide differences between indi- 
viduals that the results have very little significance. The use of 
the large field was carried as far as practicable because the tendency 
has been to use that type of photometer for all sorts of measure- 
ments, and it was desired to correlate that instrument with the 
flicker, particularly with respect to differences between individuals 
as well as relative average values for the two instruments. 


The preceding sections cover the primary purposes of this work, 
which was to establish an average eye and to test the usefulness 
of the proposed method of selecting observers by having a large 
number make measurements on the test solutions and on some 
typical color difference. The following sections give the results 
of measurements by a few observers with several other degrees of 
color difference. The observers were selected from those con- 
veniently available, the principal purpose being to secure a wide 
range of individual characteristics in order to illustrate the appli- 
cation of the method of selection. Only a few measurements were 
made, and the results are intended to be qualitative demonstra- 
tions of the method, not precise determinations of the things 


This color difference is so great that most observers showed 
marked fluctuation in results from day to day with the equality 
photometer, although the majority made fairly good settings at 
any one time. Eleven observers made two sets on both pho- 
tometers, using only the large field on the equality of brightness. 
On it each set consisted of three separate groups of readings, while 
on the flicker only two groups were made for each set, but the 
equality results were so erratic that the whole series of measure- 
ments with it were repeated. The individual sets are shown in 
Fig. 5. The circles crossed by a line indicate sets in which means 
of groups showed marked discrepancies among themselves. The 
mean of the equality-of-brightness sets is about 5 per cent above 

Rkhtmy^] An Average Eye and Comparison of Photometers 


the flicker curve, but the only observers who repeated values at all 
consistently from day to day fall closer to that curve, and the most 
consistent observer has all four sets below it. Nevertheless, even 
if the more erratic sets are discarded, the equality values are defi- 
nitely higher than those obtained by the flicker method. 

.11 fib LOO 



Fig. 5. — Transmission of 1 cm cell of 75 per cent concentration Ives-Kingsbury nickel- 
ammonium sulphate solution 

The crossed circles indicate measurements in which the groups of readings differed greatly. These are 
disregarded in drawing the curve. The published equation for transmission of this solution gives a value 
of 0.397 for this concentration 

For a ratio of 0.99 the mean transmission by the flicker pho- 
tometer is 0.397; by the equality (including all sets) 0.417, the 
mean residuals being 0.8 per cent and 3.5 per cent. The slope of 
the flicker curve indicates a change in transmission of 0.38 per 
cent for 1 per cent difference in ratio. 

It may be noted that this solution is the 75 per cent concen- 
tration of Ives and Kingsbury's blue working solution, 12 for which 

"Trans. 111. Eng. Soc, 10, p. 253; 1915. 


Bulletin of the Bureau of Standards 


the trar. a calculated from the published equation is c 

as determined for a characteristic ratio of unity, which should 
give 0.399 for a ratio of 0.99. The difference between the original 
calibration and the present check on this one point with the flicker 
photometer is therefore one-half per cent. There are no other 
equality -of -brightness measurements available for comparison. 
Some further measurements on this solution are given in a later 
section of this paper. 


\g. 6 shows similar data for the comparison of a carbon lamp 
with a standard operated to match the pentane lamp flame in 

. :/ Br. :,:-.: -,ess 


using a 4 *pc carbon standard 


color. This is in the neighborhood of 7.5 wpc. Here the slope is 
rsed because the light measured is redder than that of the 
carbon lamp, and the change in observed candlepower corre- 
sponding to 1 per cent in ratio is o. 1 per cent. 

Each observer made two sets on each photometer, a set on the 
equality consisting of three groups of readings, but on the flicker 
of only two groups. The average difference between the two sets 
on the flicker was 0.6 per cent, on the equality- 1.2 per cent, the 

RichtmyZ\ An Average Eye and Comparison of Photometers 107 

average residuals (departures from the curve) being 0.4 per cent 
and 0.9 per cent. In the two measurements of the characteristic 
ratio made by each observer the average difference was as usual 
1 per cent. 

The mean value obtained on the equality is 0.6 per cent below 
that given by the flicker photometer, and that this is not entirely 
due to accidental variation is indicated by the fact that 10 of the 
12 observers varied in this direction. 

The actual candlepowers found were 8.75 by the flicker and 
8. 70 by the equality photometer for a lamp whose value had 
previously been established as 8.70 by repeated calibrations in 
comparison with 4 wpc standards on the standard Lummer- 
Brodhun photometer. 



At the completion of this work the lamps which had been meas- 
ured at various laboratories, as reported by Middlekauff and Skog- 
land, 13 were available, and in order to obtain a direct comparison 
of further flicker values with the results of those measurements a 
few sets were made on the lamps at different voltages. As a con- 
venient means of making the measurements with the standard 
illumination on the flicker photometer, the values for the lamps 
were obtained indirectly by first calibrating, with the flicker pho- 
tometer, cells filled with properly chosen concentrations of the 
Ives- Kingsbury blue solution, which has already been mentioned, 
and then measuring the lamp on the Iyummer-Brodhun photometer 
with approximate color match obtained by the cells. This pro- 
cedure also gave a check on the calibration of that solution as 
published. The measurements made on each concentration of 
the solution were four sets by each of three observers, with slight 
corrections to put the results on the basis of the average eye giving 
a characteristic ratio of 0.99. The results are given in Table 4, 
the transmissions being percentages of the transmission of a similar 
cell filled with water. The values in column 4 are calculated from 
Ives and Kingsbury's equation. These values for transmission all 
refer to the transmission for light similar in quality to that of a 
4 wpc carbon lamp. 

la Trans. 111. Eng. Soc, 11, p. 164, 1916; this Bulletin, 13, p. 2S7, Sci. Paper No. 277. 

io8 Bui ni oj Standards 

Transmission of 1 cm Cells with Ives-Kingsbury Blue Solution 

[VU. 14 

Equivalent watts per candle 

Concentra- Observed Calculated f* 1 ^*!** 1 

tion transmis- transmis- tra ^^ a " 

sion sion „ ~» 


cf nMIm 












Since the original calibration was supposedly based on an average 
eye corresponding to a characteristic ratio of i.oo, the degree of 
concordance obtained should be judged, perhaps, by comparison of 
columns 3 and 5, but as absolute calibrations of the solution col- 
umns 3 and 4 should be taken, and within the uncertainty of the 
present determinations made by the small number of observers 
mentioned, the equation from which column 4 is calculated 
r= -0.539c 1 ' 03 ) is correct. 

The last four of these solutions were used in measuring the lamps. 
75 per cent concentration is very much bluer than is required 
by any of the voltages at which these lamps were measured in the 
comparison between different laboratories, and it was included 
only for a more complete comparison with the calibration curve 
and with the previous measurements by a larger number of 
observers. (See Fig. 5). 

The results on the lamps are best shown, perhaps, by compari- 
son with those calculated from the Middlekauff-Skogland equa- 
tions, 14 which are based on measurements made with the standard 
Lummer-Brodhun photometer. The following table shows the 
percentage departure of the values found at the different efficien- 
cies from the calculated values for each lamp. These measure- 
ments are equivalent to the direct comparison of lamps at the 
different efficiencies with a 4 wpc carbon lamp. The differences 
given are positive when the flicker values are lower. 

Differences Between Standard Lummer-Brodhun and Flicker Photometer Values 

Approximate wpc . 

Lamp 1 

Lamp 2 

-: 4S 


This Bulletin, 11, p. 4J3, Sci. Paper No. 23S; Trans. Ilium. Eng. Soc, 9, p. 734, 1914- 

RkhtmyS\ An Average Eye and Comparison of Photometers 109 

The large departure at 1 wpc is quite inconsistent with all other 
measurements, and unfortunately the other lamp was not meas- 
ured at this efficiency. The course of the variation probably 
should be considered independently of this point. The color 
match obtainable with this solution is far from being perfect, but 
the variations arising from this cause are not sufficient to explain 
the departure of this point from the other measurements. The 
significance of these measurements can best be seen by referring 
to the more recent paper by Middlekauff and Skogland, which 
includes them with results from other laboratories. It may be 
said that they agree very well with values obtained by Ives 
using a luminosity scale based on the flicker photometer but fall 
considerably below all the results obtained with the usual I^ummer- 
Brodhun photometer. The measurements already reported on 
the 75 per cent concentration of the solution indicate that this 
difference probably will continue to increase as comparisons are 
carried to higher efficiencies. 


The preceding results emphasize the fact that for accurate 
heterochromatic measurements a systematic choice of observers 
is essential. The system proposed by Ives and Kingsbury appears 
to be practical and reliable at least for color differences of the 
type dealt with in these tests. The average eye established is 
represented by a value of approximately 0.99 for the ratio of the 
transmission of the yellow test solution to that of the blue solu- 
tion under the specified conditions. The agreement with the 
original ratio assigned (1.00) is very good, especially since the 
latter was largely based on an indirect derivation of the average 
eye. It is suggested, however, that if the lack of symmetry in 
the distribution of these observers (as indicated by Fig. 2) is 
found to persist when larger numbers of observers are included 
greater reproducibility of the normal ratio might be obtained by 
choosing as the normal not the average value but the median, 
which in this case is approximately 0.98. 

The differences in observed values arising from individual 
peculiarities of course increase as the color difference increases. 
When comparisons are made directly with a 4 wpc carbon lamp, 
a difference of 1 per cent in the characteristic ratios of observers 
should result in approximately the following differences in observed 


Bulletin of the Bureau of Sta?idards 

[Vol. 14 

candlepower of a tungsten lamp at the various specific consump- 
tions given : 

Watts per 

Per cent 






When plotted in terms of lumens per watt, these data give 
nearly a straight line. 

Fig. 7 shows the percentage deviation from normal values as a 
function of the characteristic ratio for the several color differences 


n .96 1.00 104 

108 112 

Fig. 7. — Deviation from normal values corresponding to different test ratios when the 
light indicated is compared with that of a 4 wpc carbon lamp 

1. 0.75 concentration blue solution with carbon lamp, equivalent to tungsten lamp at about 0.65 wpc. 
The curve for the blue test solution practically coincides with this. 2. 1.2 wpc tungsten. 3. Color match, 
4 wpc carbon or 3.1 wpc tungsten. 4. Pentanelamp. 5. Yellow test solution 

indicated. Thus, an observer whose characteristic 

ratio — is 

0.90, in measuring the candlepower of a 1.2 wpc tungsten lamp 
against a 4 wpc carbon lamp (3.1 wpc tungsten) would assign to 
the tungsten lamp a value 1.2 per cent too high. To a 0.65 wpc 
tungsten lamp he would assign a value 3.5 per cent too high. Of 
the 1 1 4 observers 19(17 per cent) would have obtained values for 
a 1.2 wpc tungsten lamp differing 1 per cent or more from the 

RicSyeA An Average Eye and Comparison of Photometers in 

normal value; 70 (61 per cent) would have departed 1 per cent 
or more from the normal value in measuring a 0.65 wpc tungsten 

For measurements on color differences of this type it is not 
necessary to have a group of observers whose average ratio is 
normal; any observers may be used and their results corrected to 
the normal by use of curves similar to Fig. 7. These curves can 
be summarized by the equation 

/- I 

n i+m(R-R n ) 

where I Q is the normal value of a photometric quantity (such as 
candlepower, illumination, or transmission), R n is the normal 
characteristic or "test" ratio, while / and R are the values of 
these quantities found by a particular observer, m is an empirical 
constant, which may be either positive or negative and which de- 
pends on the color difference involved in the observation. It is 
the slope of the curves in Fig. 7. There may be slight systematic 
errors in the corrected values; that is, some observers may be 
always off the curve in the same direction, and consequently a 
number of observers should be used for highly accurate results. 
Not enough repeated measurements are at hand to show with 
certainty the average magnitude of these systematic errors, but 
they are certainly small in most cases. 

On the average, measurements made with an equality-of- 
brightness photometer will show practically the same differences 
due to individual characteristics as those made with the flicker, 
but the erratic variations are often so great as to overshadow these 
systematic differences. It has been remarked that some ob- 
servers develop the ability to make very consistent settings on the 
equality photometer. In the majority of cases such observers 
have been found to read close to the value indicated by their test 
ratio, but this is not always the case. 


With regard to certainty of measurement the flicker photo- 
meter shows a decided advantage even with small color differ- 
ences. With more experienced observers, specially selected, this 
advantage would probably be materially reduced, but would not 
be entirely lost, because even when an observer makes consistent 
settings on the equality photometer the relation of his settings to 
those of the normal observer is uncertain. 

20172°— 17 8 

1 1 2 Bulletin of the Bureau of Standards [va. n 

Trained observers are needed with either photometer, but with 
the flicker any observer of fair ability can make definite sets even 
with large color differences, whereas on the Lummer-Brodhun pho- 
tometer it is only the exceptional observer who can do so. Exten- 
sive investigations at the English National Physical Laboratory 15 
indicate that the final certainty of results is not increased by 
using the laborious "cascade" or step-by-step method of meas- 
urements to avoid sets with large color difference. Little is 
gained by such a procedure, unless the results of successive steps 
are agreed upon and made a practically independent standard 
for future use. This is the tendency of the present practice, and 
it appears that by this method fairly satisfactorily standards of 
successively higher and higher temperature may eventually be 
agreed upon by inter laboratory and international comparisons. 
Xo one can say with what degree of accuracy the values of these 
standards can be reproduced from the fundamental standards a 
few years hence, and of course, this method applies only to those 
color differences which can be thus built up step by step with 
concrete standards to preserve the values at each step. 

The flicker photometer, on the other hand, affords a means of 
relatively precise comparison between lights of all degrees of color 
difference and makes possible the use of test readings for which 
average values, which should be highly reproducible, can be 

In regard to relative results there appears to be no room for 
doubt that for sources having relatively high intensity at the blue 
end of the spectrum the values given by the flicker photometer 
as here used depart appreciably from those obtained with the 
Lummer-Brodhun as used in common practice, the difference 
probably being of the order of 3 per cent at the higher efficiencies 
reached by the present gas-filled lamps. It is, however, hardly 
proper to assume that the results obtained by either photometer 
are "right" and anything different is "wrong." The equality-of- 
brightness method of measurement is undoubtedly more closely 
related to the way in which the light is used, but it is by no means 
established that that method correctly indicates the relative use- 
fulness of two kinds of light. It must be recognized that there 
is no one definite "correct" ratio between the intensities of two 
lights of different color. The relative candlepowers assigned to 
a carbon and a tungsten lamp, for example, depend to some extent 

15 Paterson and Dudding. Proc. Phys. Soc, London, 27, p. 163, 1915; and Phil. Mag. (6), SO, p. 63, 1915- 

Richtmy£\ An Average Eye and Comparison of Photometers 113 

on the conditions under which the measurements are made. The 
specification of conditions of measurement must be more or less 
arbitrary, and the results obtained can not be expected to be an 
exact indication of the value of different kinds of light under 
different conditions. Before we shall know much about the 
relative usefulness of different kinds of light much more experi- 
mental work must be done. An important prerequisite for such 
investigations or any others involving the comparison of the 
intensity of lights of very different color is a method which will 
enable different experimenters to make consistent measurements 
of the quantity which must serve as a basis for the comparison 
of their results. The usual equality-of -brightness method of 
comparison certainly does not fulfill this requirement. The flicker 
photometer at present furnishes the most promising method 

For the standardizing laboratory, which is expected to reproduce 
results after the lapse of years when the observers available may 
be entirely different, the flicker photometer (used under definitely 
specified conditions), with a systematic method of determining 
the relation of each observer to the normal, promises to give to 
heterochromatic photometry a certainty which has appeared quite 
unattainable with other instruments. Besides giving this probable 
increased certainty in future reproduction of values, it reduces 
considerably the labor necessary to attain a given accuracy at the 
present time. Comparison of actual tests made in the routine 
work of the laboratory shows that even with relatively small color 
differences a given accuracy of reproduction of results requires 
several times as many measurements with the equality-of- 
brightness or the contrast photometer as with the flicker. 

The authors are deeply indebted for the cordial assistance of 
many associates which has made possible the collection of the 
data presented. Particular acknowledgement is due to A. H. 
Taylor and E. M. Baker, who assisted in all of the work. 

Washington, January 15, 191 6. 

■ ■